# Supervised Quantile Normalisation

## TL;DR

This paper introduces SUQUAN, a method that jointly optimizes the target distribution in quantile normalisation with the analysis model, improving performance across various data types.

## Contribution

It proposes a novel approach to couple quantile normalisation with analysis, optimizing the target distribution for better results.

## Key findings

- SUQUAN outperforms standard quantile normalisation on simulated data.
- The method is effective on images and genomic data.
- It leads to a low-rank matrix regression formulation.

## Abstract

Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after normalisation, they follow the same target distribution for each sample. Choosing a "good" target distribution remains however largely empirical and heuristic, and is usually done independently of the subsequent analysis of normalised data. We propose instead to couple the quantile normalisation step with the subsequent analysis, and to optimise the target distribution jointly with the other parameters in the analysis. We illustrate this principle on the problem of estimating a linear model over normalised data, and show that it leads to a particular low-rank matrix regression problem that can be solved efficiently. We illustrate the potential of our method, which we term SUQUAN, on simulated data, images and genomic data, where it outperforms standard quantile normalisation.